Solve for a
a=\frac{x\left(7y+b\right)}{2y}
x\neq 0\text{ and }y\neq 0
Solve for b
b=\frac{y\left(2a-7x\right)}{x}
x\neq 0\text{ and }y\neq 0
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y\times 2a-xb=7xy
Multiply both sides of the equation by xy, the least common multiple of x,y.
y\times 2a=7xy+xb
Add xb to both sides.
2ya=bx+7xy
The equation is in standard form.
\frac{2ya}{2y}=\frac{x\left(7y+b\right)}{2y}
Divide both sides by 2y.
a=\frac{x\left(7y+b\right)}{2y}
Dividing by 2y undoes the multiplication by 2y.
y\times 2a-xb=7xy
Multiply both sides of the equation by xy, the least common multiple of x,y.
-xb=7xy-y\times 2a
Subtract y\times 2a from both sides.
-xb=7xy-2ya
Multiply -1 and 2 to get -2.
\left(-x\right)b=7xy-2ay
The equation is in standard form.
\frac{\left(-x\right)b}{-x}=\frac{y\left(7x-2a\right)}{-x}
Divide both sides by -x.
b=\frac{y\left(7x-2a\right)}{-x}
Dividing by -x undoes the multiplication by -x.
b=\frac{2ay}{x}-7y
Divide y\left(7x-2a\right) by -x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}